A Novel Method for Optimal Solution of Fuzzy Chance Constraint Single-Period Inventory Model

A method is proposed for solving single-period inventory fuzzy probabilistic model (SPIFPM) with fuzzy demand and fuzzy storage space under a chance constraint. Our objective is to maximize the total profit for both overstock and understock situations, where the demand D~j for each product j in the objective function is considered as a fuzzy random variable (FRV) and with the available storage space area W~, which is also a FRV under normal distribution and exponential distribution. Initially we used the weighted sum method to consider both overstock and understock situations. Then the fuzziness of the model is removed by ranking function method and the randomness of the model is removed by chance constrained programming problem, which is a deterministic nonlinear programming problem (NLPP) model. Finally this NLPP is solved by using LINGO software. To validate and to demonstrate the results of the proposed model, numerical examples are given

Forecasting of Service Parts Based on Fuzzy Reliability of the Product

This paper presents a forecasting model depends on the reliability of product and the failure of its parts to forecast the required quantity of spare parts. Fuzzy logic is integrated with the forecasted model to treat the uncertainty that may be exist around defining the parameters values. Fuzzification of the product reliability is constructed using alpha cut and triangular fuzzy number. The effect of fuzzy process on the forecasted required demand of spare parts will be studied in three cases: 1) fuzzification of the mean of the product reliability, 2) fuzzification of the standard deviation of the product reliability, and 3) fuzzification of both the mean and standard deviation of the product reliability. Four suggested defuzzification methods (mean-max, centroid, signed distance, and graded mean integration representation) were used to figure out the difference between the crisp and the fuzzy forecasted demand with its related costs and to save the stock with the suitable production ranges. From the results, the maximum deviation between the crisp and the fuzzy forecasted demand was resulted from the fuzzification of both the mean and the standard deviation with percentage range from 2.06 up to 5.45 that would save the non-stock out than crisp forecasting

Forecasting of Service Parts Based on Fuzzy Reliability of the Product

This paper presents a forecasting model depends on the reliability of product and the failure of its parts to forecast the required quantity of spare parts. Fuzzy logic is integrated with the forecasted model to treat the uncertainty that may be exist around defining the parameters values. Fuzzification of the product reliability is constructed using alpha cut and triangular fuzzy number. The effect of fuzzy process on the forecasted required demand of spare parts will be studied in three cases: 1) fuzzification of the mean of the product reliability, 2) fuzzification of the standard deviation of the product reliability, and 3) fuzzification of both the mean and standard deviation of the product reliability. Four suggested defuzzification methods (mean-max, centroid, signed distance, and graded mean integration representation) were used to figure out the difference between the crisp and the fuzzy forecasted demand with its related costs and to save the stock with the suitable production ranges. From the results, the maximum deviation between the crisp and the fuzzy forecasted demand was resulted from the fuzzification of both the mean and the standard deviation with percentage range from 2.06 up to 5.45 that would save the non-stock out than crisp forecasting

Applying nonlinear MODM model to supply chain management with quantity discount policy under complex fuzzy environment

Purpose: The aim of this paper is to deal with the supply chain management (SCM) with quantity discount policy under the complex fuzzy environment, which is characterized as the bi-fuzzy variables. By taking into account the strategy and the process of decision making, a bi-fuzzy nonlinear multiple objective decision making (MODM) model is presented to solve the proposed problem. Design/methodology/approach: The bi-fuzzy variables in the MODM model are transformed into the trapezoidal fuzzy variables by the DMs's degree of optimism ?1 and ?2, which are de-fuzzified by the expected value index subsequently. For solving the complex nonlinear model, a multi-objective adaptive particle swarm optimization algorithm (MO-APSO) is designed as the solution method. Findings: The proposed model and algorithm are applied to a typical example of SCM problem to illustrate the effectiveness. Based on the sensitivity analysis of the results, the bi-fuzzy nonlinear MODM SCM model is proved to be sensitive to the possibility level ?1. Practical implications: The study focuses on the SCM under complex fuzzy environment in SCM, which has a great practical significance. Therefore, the bi-fuzzy MODM model and MO-APSO can be further applied in SCM problem with quantity discount policy. Originality/value: The bi-fuzzy variable is employed in the nonlinear MODM model of SCM to characterize the hybrid uncertain environment, and this work is original. In addition, the hybrid crisp approach is proposed to transferred to model to an equivalent crisp one by the DMs's degree of optimism and the expected value index. Since the MODM model consider the bi-fuzzy environment and quantity discount policy, so this paper has a great practical significance.Peer Reviewe

The Fuzzy Economic Order Quantity Problem with a Finite Production Rate and Backorders

The track of developing Economic Order Quantity (EOQ) models with uncertainties described as fuzzy numbers has been very lucrative. In this paper, a fuzzy Economic Production Quantity (EPQ) model is developed to address a specific problem in a theoretical setting. Not only is the production time finite, but also backorders are allowed. The uncertainties, in the industrial context, come from the fact that the production availability is uncertain as well as the demand. These uncertainties will be handled with fuzzy numbers and the analytical solution to the optimization problem will be obtained. A theoretical example from the process industry is also given to illustrate the new model